testy.sh

#!/bin/bash

echo == example the first ==

f1() {
  local v=1

  echo f1: $v
  f2
}

f2() {
  echo f2: $v
}

v=0
f1

echo == example the second ==

v=0

f1() {
  local v=1
  echo f1-pre: $v
  f2
  echo f1-post: $v
}

f2() {
  v=2
}

f1
echo global: $v

the-docs.md

The docs that are Very Wrong:

A variable declared as local is one that is visible only within the block of code in which it appears. It has local scope. In a function, a local variable has meaning only within that function block. [1]